Eighth-order magnetic moment of the electron. III. Sixth-order vertices containing a second-order vacuum polarization subdiagram

We have calculated the contribution to the eighth-order anomalous magnetic moment of the electron arising from 150 Feynman diagrams, each generated by inserting a second-order vacuum polarization loop in the photon lines of sixth-order vertices of the three-photon-exchange type. Our result is $1.419\left(16\right)\mathrm{}{\left(\frac{\alpha }{\pi }\right)}^4$. The theoretical error represents the estimated accuracy (90% confidence limit) of the required numerical integrations.